Using continuation methods from the integrable Ablowitz-Ladik lattice, we
have studied the structure of numerically exact mobile discrete breathers in
the standard Discrete Nonlinear Schrodinger equation. We show that, away from
that integrable limit, the mobile pulse is dressed by a background of resonant
plane waves with wavevectors given by a certain selection rule. This background
is seen to be essential for supporting mobile localization in the absence of
integrability. We show how the variations of the localized pulse energy during
its motion are balanced by the interaction with this background, allowing the
localization mobility along the lattice.Comment: 10 pages, 11 figure
